Wavelet-based multiresolution analysis of irregular surface meshes
Wavelet-based multiresolution analysis of irregular surface meshes
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DOI：
10.1109/tvcg.2004.1260763
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发表时间：
2004-03
影响因子：
5.2
通讯作者：
S. Valette;R. Prost
中科院分区：
文献类型：
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作者：
S. Valette;R. Prost
我们扩展Lounsbery的多分辨率分析小波为基础的理论，三角形的三维网格，它只能适用于定期细分的网格，从而涉及到现有的三维数据的重新网格化。基于一种新的不规则细分方案，该算法可以直接应用于不规则网格，这可能是非常有趣的，当一个人想要保持处理后的网格的连通性和几何形状完全不变。这在CAD（计算机辅助设计）中非常方便，当网格具有纹理和颜色信息等属性时，或者当3D网格用于模拟时，以及不同的连接性可能导致模拟错误时。该算法面临的逆问题，提出了解决方案。对于每一个分辨率级别，简化处理，以保持网格尽可能规则。此外，几何准则用于保持近似的几何形状尽可能接近原始网格。在各种参考网格上的几个例子证明了我们的建议的效率。
We extend Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (computer-assisted design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.